回溯法生活中应用代码举例

下面是一个生活中应用回溯法的示例代码：解数独问题。

数独是一种数学智力游戏，玩家需要在 9x9 的网格中填入数字，使得每一行、每一列和每一个 3x3 的宫（共 9 个）内的数字都是 1~9 的不同数字。如果你遇到了数独难题，可以使用回溯算法来解决。

下面是使用回溯算法解决数独问题的示例代码：

def solve_sudoku(board):
    """
    解数独问题
    :param board: 数独题目，是一个 9x9 的二维数组
    :return: 如果存在解，则返回解，否则返回 None
    """
    def backtrack(board, row, col):
        if col == 9:
            # 进入下一行
            return backtrack(board, row + 1, 0)
        if row == 9:
            # 找到解
            return True
        if board[row][col] != '.':
            # 当前位置已经有数字，跳过
            return backtrack(board, row, col + 1)
        for num in range(1, 10):
            if not is_valid(board, row, col, str(num)):
                continue
            board[row][col] = str(num)
            if backtrack(board, row, col + 1):
                return True
            board[row][col] = '.'
        return False

    def is_valid(board, row, col, num):
        for i in range(9):
            if board[row][i] != '.' and board[row][i] == num:
                return False
            if board[i][col] != '.' and board[i][col] == num:
                return False
            if board[3 * (row // 3) + i // 3][3 * (col // 3) + i % 3] != '.' and board[3 * (row // 3) + i // 3][3 * (col // 3) + i % 3] == num:
                return False
        return True

    if backtrack(board, 0, 0):
        return board
    else:
        return None

使用方法：

board = [
    ["5", "3", ".", ".", "7", ".", ".", ".", "."],
    ["6", ".", ".", "1", "9", "5", ".", ".", "."],
    [".", "9", "8", ".", ".", ".", ".", "6", "."],
    ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
    ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
    ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
    [".", "6", ".", ".", ".", ".", "2", "8", "."],
    [".", ".", ".", "4", "1", "9", ".", ".", "5"],
    [".", ".", ".", ".", "8", ".", ".", "7", "9"]
]

solution = solve_sudoku(board)

if solution:
    for row in solution:
        print(row)
else:
    print("No solution")

输出：

['5', '3', '4', '6', '7', '8', '9', '1', '2']
['6', '7', '2', '1', '9', '5', '3', '4', '8']
['1', '9', '8', '3', '4', '2', '5', '6', '7']
['8', '5', '9', '7', '6', '1', '4', '2', '3']
['4', '2', '6', '8', '5', '3', '7', '9', '1']
['7', '1', '3', '9', '2', '4', '8', '5', '6']
['9', '6', '1', '5', '3', '7', '2', '8', '4']
['2', '8', '7', '4', '1', '9', '6', '3', '5']
['3', '4', '5', '2', '8', '6', '1', '7', '9']